The angular dependence of the multipole-multipole interaction for energy transfer

The interaction between multipoles is not isotropic even in cubic systems. This results in the introduction of geometric reduction factors in the calc ulation of energy-transfer rates in crystals. We derive these reduction fac tors for the cases of dipole-dipole, dipole-quadrupole, and quadrupole-quad rupole couplings and present a general procedure for their derivation in ot her cases. For the dipole-dipole case the geometric factor is independent o f the distribution of the acceptor species. but for higher-order couplings, a significant angular dependence is found.